Could I get a longer wrench please?

Classical Mechanics Level 5

A fastener is a system of 2 objects - a bolt and a nut. You come across such a bolt/nut system tightened all the way, so that the nut and the top of the bolt are pressing against each other with a force of 5 N. If the nut is held fixed, how much torque in mJ does one need to put on the bolt to begin to unscrew it?

Details and assumptions

  • The radius of the bolt is \(R = 2\) mm.
  • The threads on the bolt are such that the bolt needs to rotate N = 20 cycles to move \(d = 1~cm\) vertically away from the nut.
  • The friction coefficient between the bolt and nut is \(k = 0.5 \).

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